1
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Li J, Zhang B, Li Y. Glass Formation in Mechanically Interlocked Ring Polymers: The Role of Induced Chain Stiffness. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c01368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Jian Li
- Department of Physics and Electronic Engineering, Heze University, Heze274015, China
| | - Bokai Zhang
- School of Physical Science and Technology, Southwest University, Chongqing400715, China
- Department of Physics, Zhejiang Sci-Tech University, Hangzhou310018, China
| | - Yushan Li
- Department of Physics and Electronic Engineering, Heze University, Heze274015, China
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2
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Tejedor AR, Carracedo R, Ramírez J. Molecular dynamics simulations of active entangled polymers reptating through a passive mesh. POLYMER 2023. [DOI: 10.1016/j.polymer.2023.125677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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3
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Zheng Y, Tsige M, Wang SQ. Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening. Macromol Rapid Commun 2023; 44:e2200159. [PMID: 35881534 DOI: 10.1002/marc.202200159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 06/20/2022] [Indexed: 01/11/2023]
Abstract
In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (WiR >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as WiR > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.
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Affiliation(s)
- Yexin Zheng
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Mesfin Tsige
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Shi-Qing Wang
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
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4
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Dietz JD, Kröger M, Hoy RS. Validation and Refinement of Unified Analytic Model for Flexible and Semiflexible Polymer Melt Entanglement. Macromolecules 2022; 55:3613-3626. [PMID: 35571224 PMCID: PMC9097689 DOI: 10.1021/acs.macromol.1c02597] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Revised: 03/23/2022] [Indexed: 11/28/2022]
Abstract
We combine molecular dynamics simulations and topological analyses (TA) to validate and refine a recently proposed unified analytic model [Hoy, R. S.; Kröger, M. Phys. Rev. Lett. 2020, 124, 147801] for the reduced entanglement length, tube diameter, and plateau modulus of polymer melts. While the functional forms of the previously published expressions are insensitive to the choice of the TA method and N e -estimator, obtaining better statistics and eliminating all known sources of systematic error in the N e -estimation alters their numerical coefficients. Our revised expressions quantitatively match bead-spring simulation data over the entire range of chain stiffnesses for which systems remain isotropic, semiquantitatively match all available experimental data for flexible, semiflexible, and stiff polymer melts (including new data for conjugated polymers that lie in a previously unpopulated stiffness regime), and outperform previously developed unified scaling theories.
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Affiliation(s)
- Joseph D. Dietz
- Department of Physics, University of South Florida, Tampa, Florida 33620, United States
| | - Martin Kröger
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Robert S. Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, United States
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5
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Ma J, Carrillo JMY, Do C, Chen WR, Falus P, Shen Z, Hong K, Sumpter BG, Wang Y. Spatial correlations of entangled polymer dynamics. Phys Rev E 2021; 104:024503. [PMID: 34525580 DOI: 10.1103/physreve.104.024503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 08/03/2021] [Indexed: 11/07/2022]
Abstract
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
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Affiliation(s)
- Jihong Ma
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Changwoo Do
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Wei-Ren Chen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Péter Falus
- Institut Laue-Langevin, B.P. 156, F-38042 Grenoble CEDEX 9, France
| | - Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kunlun Hong
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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6
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Steenbakkers RJA, Andreev M, Schieber JD. Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model. Phys Rev E 2021; 103:022501. [PMID: 33736108 DOI: 10.1103/physreve.103.022501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Accepted: 12/09/2020] [Indexed: 11/07/2022]
Abstract
We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.
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Affiliation(s)
- Rudi J A Steenbakkers
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 35th Street, Chicago, Illinois 60616, USA
| | - Marat Andreev
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Physics, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, Illinois 60616, USA
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 35th Street, Chicago, Illinois 60616, USA.,Department of Physics, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Street, Chicago, Illinois 60616, USA
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7
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Determine tube diameter by measuring entropy tensile force. JOURNAL OF POLYMER RESEARCH 2020. [DOI: 10.1007/s10965-020-02301-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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8
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G. Cunha MA, Robbins MO. Effect of Flow-Induced Molecular Alignment on Welding and Strength of Polymer Interfaces. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01508] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Marco A. G. Cunha
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Mark O. Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
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9
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Tejedor AR, Ramírez J. Dynamics of entangled polymers subjected to reptation and drift. SOFT MATTER 2020; 16:3154-3168. [PMID: 32159579 DOI: 10.1039/d0sm00056f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this work we formulate a model to study the dynamical response of entangled polymers subjected to a constant drift. The drift may originate from an internal activity that acts along the primitive path of the tube. Here, we expand our previous work (A. R. Tejedor and J. Ramirez, Macromolecules, 2019, 52, 8788-8792) and solve analytically the most significant observables of the theory, providing explicit results to observables not considered previously, such as the tangent-tangent correlation function and the dynamic structure factor. These analytical results are compared and verified by means of Brownian dynamics simulations of the tube model. Interestingly, while the mean squared displacement of the chain segments is always subdiffusive, the center of mass shows a superdiffusive regime when the magnitude of the drift is significant. We provide scaling arguments to explain this phenomenon. We also consider the effect of contour-length fluctuations and describe two different approaches to introduce a drift using active particles.
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Affiliation(s)
- Andrés R Tejedor
- Department of Chemical Engineering, Universidad Politécnica de Madrid, José Gutiérrez Abascal 2, 28006, Madrid, Spain.
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10
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Rauscher PM, Schweizer KS, Rowan SJ, de Pablo JJ. Thermodynamics and Structure of Poly[n]catenane Melts. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02706] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Phillip M. Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States
| | - Kenneth S. Schweizer
- Department of Materials Science, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, United States
- Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, United States
- Department of Chemical and Biomolecular Engineering, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, United States
- Department of Chemistry, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, United States
| | - Stuart J. Rowan
- Pritzker School of Molecular Engineering, University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States
- Department of Chemistry, University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States
- Chemical and Engineering Sciences, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States
- Center for Molecular Engineering, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States
- Center for Molecular Engineering, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States
- Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States
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11
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Hou JX. Microscopic topology of entangled polymeric liquids. POLYMER 2020. [DOI: 10.1016/j.polymer.2019.122033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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12
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Hsu HP, Kremer K. Clustering of Entanglement Points in Highly Strained Polymer Melts. Macromolecules 2019; 52:6756-6772. [PMID: 31534275 PMCID: PMC6740293 DOI: 10.1021/acs.macromol.9b01120] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 08/13/2019] [Indexed: 11/30/2022]
Abstract
Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead-spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.
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Affiliation(s)
- Hsiao-Ping Hsu
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
| | - Kurt Kremer
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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13
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Shanbhag S. Mathematical foundations of an ultra coarse-grained slip link model. J Chem Phys 2019; 151:044903. [PMID: 31370523 DOI: 10.1063/1.5111032] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The master equation underlying ecoSLM, an ultra-coarse-grained slip link model, is presented. In the absence of constraint release, the equilibrium and dynamic properties of the discrete master equation for large chains are found to be virtually identical to the continuous Fokker-Planck equation for Brownian particles diffusing in a potential. A single-chain microscopic model with repulsion between adjacent slip links is described. It is approximately consistent with the quadratic fluctuation potential used in ecoSLM. Mapping ecoSLM with fine-grained slip link models or experiments requires specification of an effective friction as a function of molecular weight. Methods to accomplish this are discussed. Collectively, the mathematical framework described provides an interface for fine-grained slip link models to potentially use ecoSLM for extreme coarse-graining.
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Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, USA
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14
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Cao J, Wang Z, Likhtman AE. Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks. Polymers (Basel) 2019; 11:E496. [PMID: 30960480 PMCID: PMC6473678 DOI: 10.3390/polym11030496] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Revised: 03/08/2019] [Accepted: 03/11/2019] [Indexed: 11/26/2022] Open
Abstract
Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual "slip-links", each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight N e , a key tube theory parameter, can be extracted. The procured N e value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of N e as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms μ ( t ) , or equivalently arm end-to-end vector relaxation function ϕ ( t ) , through the mean FP time spectrum τ ( s ) of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation.
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Affiliation(s)
- Jing Cao
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK.
| | - Zuowei Wang
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK.
| | - Alexei E Likhtman
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK
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15
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Ramos J, Vega J, Martínez-Salazar J. Predicting experimental results for polyethylene by computer simulation. Eur Polym J 2018. [DOI: 10.1016/j.eurpolymj.2017.12.027] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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16
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Xiao H, Luo C, Yan D, Sommer JU. Molecular Dynamics Simulation of Crystallization Cyclic Polymer Melts As Compared to Their Linear Counterparts. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01570] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Hongyi Xiao
- Department
of Physics, Beijing Normal University, 100875 Beijing, China
- Institute
Theory of Polymers, Leibniz-Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Chuanfu Luo
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China
| | - Dadong Yan
- Department
of Physics, Beijing Normal University, 100875 Beijing, China
| | - Jens-Uwe Sommer
- Institute
Theory of Polymers, Leibniz-Institute of Polymer Research Dresden, 01069 Dresden, Germany
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17
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Hou JX, Yu XC, Huang ZW. Primitive path analysis of linear polymer embedded in post array. JOURNAL OF POLYMER RESEARCH 2017. [DOI: 10.1007/s10965-017-1258-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Features of strain-induced crystallization of natural rubber revealed by experiments and simulations. Polym J 2017. [DOI: 10.1038/pj.2016.114] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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19
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Cao J, Wang Z. Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00554] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Jing Cao
- Department of Mathematics
and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, U.K
| | - Zuowei Wang
- Department of Mathematics
and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, U.K
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20
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Wang M, Likhtman AE, Olsen BD. Crossover between activated reptation and arm retraction mechanisms in entangled rod-coil block copolymers. J Chem Phys 2015; 143:184904. [PMID: 26567681 DOI: 10.1063/1.4933427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using a coarse-grained slip-spring model, the dynamics of rod-coil block copolymers is explored over a wide parameter space to fully capture the crossover between the short rod (activated reptation) and long rod (arm retraction) limits. An analytical, closed-form expression for curvilinear diffusion by activated reptation was derived by separating the drag into individual components for the rod and coil block. Curvilinear diffusion in the intermediate rod regime, where both mechanisms are important, was then found to be faster than predicted when both mechanisms are independently combined. The discrepancy in the crossover regime arises because the rod-coil copolymer's exploration of space is not accurately described by either a coil homopolymer (assumed by activated reptation) or a rod homopolymer (assumed by arm retraction). This effect is explored by tracking the rod orientation as the polymer reptates, confirming that the polymer reptates along a path that becomes more rodlike as the rod fraction is increased. Thus, activated reptation under-predicts diffusion because the rod can choose reptation paths that are more extended than the coil homopolymer by renewal of the entanglement tube from the ends. Arm retraction under-predicts diffusion because minor rotations of the rod allow some motion before full retractions of the coil block. Finally, more familiar 3-dimensional center-of-mass diffusion measurements are related to the curvilinear diffusion analysis because the ratio of these two quantities varies smoothly between the coil and rod homopolymer limits as the reptation path becomes more extended.
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Affiliation(s)
- Muzhou Wang
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Alexei E Likhtman
- School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Bradley D Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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21
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Moreira LA, Zhang G, Müller F, Stuehn T, Kremer K. Direct Equilibration and Characterization of Polymer Melts for Computer Simulations. MACROMOL THEOR SIMUL 2015. [DOI: 10.1002/mats.201500013] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Livia A. Moreira
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Guojie Zhang
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Franziska Müller
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Torsten Stuehn
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Kurt Kremer
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
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22
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Lu Y, An L, Wang SQ, Wang ZG. Molecular Mechanisms for Conformational and Rheological Responses of Entangled Polymer Melts to Startup Shear. Macromolecules 2015. [DOI: 10.1021/ma502236m] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Yuyuan Lu
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Shi-Qing Wang
- Department
of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States
| | - Zhen-Gang Wang
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
- Division
of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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23
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Wang M, Likhtman AE, Olsen BD. Tube Curvature Slows the Motion of Rod-Coil Block Copolymers through Activated Reptation. ACS Macro Lett 2015; 4:242-246. [PMID: 35596415 DOI: 10.1021/mz5007377] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Understanding the dynamics of molecules with complex shapes is important as researchers develop advanced materials using hybrid molecules. This study applies a slip-spring model to visualize and quantify the entangled dynamics of rod-coil block copolymers. The parameters of the model are determined by matching with molecular dynamics simulation results. By monitoring the positions of polymers along the entanglement tube, rod-coil copolymers are shown to disfavor configurations where the rod occupies curved portions of the tube of randomly varying curvature created by the coil ends. This confirms that reptation of copolymers occurs by an activated mechanism and is the first demonstration of the activation barriers that have been previously inferred through diffusion measurements by simulation and experiment. The barriers to diffusion are further quantified by considering the curvilinear motion of ring polymers, and their effect on diffusion is quantitatively captured by considering one-dimensional motion along an entanglement tube with a rough free energy potential.
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Affiliation(s)
- Muzhou Wang
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Alexei E. Likhtman
- School
of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - Bradley D. Olsen
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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24
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Affiliation(s)
- Jing Cao
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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25
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Panagiotou E, Kröger M. Pulling-force-induced elongation and alignment effects on entanglement and knotting characteristics of linear polymers in a melt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042602. [PMID: 25375516 DOI: 10.1103/physreve.90.042602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Indexed: 06/04/2023]
Abstract
We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, the writhe of the chains and their PPs and the writhe of the entanglement strands all suggest a different response at the length scale of entanglement strands than that of the chains themselves and of the corresponding PPs. Our findings indicate that the chains first stretch at the level of entanglement strands and next the PP (tube) gets oriented with the "flow." These two phases of the extension and alignment of the chains coincide with two phases related to the disentanglement of the chains. Soon after the onset of external force the PPs attain a more entangled conformation, and the number of nontrivially linked end-to-end closed chains increases. Next, the chains disentangle continuously to attain an almost unentangled conformation. Using the linking matrix of the chains in the melt, we furthermore show that these phases are accompanied by a different scaling of the homogeneity of the global entanglement in the system. The homogeneity of the end-to-end closed chains first increases to a maximum and then decreases slowly to a value characterizing a completely unlinked system.
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Affiliation(s)
- E Panagiotou
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - M Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
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26
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Lu Y, An L, Wang SQ, Wang ZG. Origin of Stress Overshoot during Startup Shear of Entangled Polymer Melts. ACS Macro Lett 2014; 3:569-573. [PMID: 35590729 DOI: 10.1021/mz500260h] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Using Brownian dynamics simulation, we determine the chain orientation and stretching and their connection to stress overshoot in an entangled polymer melt undergoing startup shear at rates lower than the reciprocal of the Rouse time yet higher than the reciprocal of the reptation time. In this rate regime, the prevailing tube theory attributes the stress overshoot to alignment of the primitive chain. In contrast, our results reveal that there is substantial chain stretching that persists well beyond the Rouse time, and it contributes significantly to the initial stress growth. In particular, stress overshoot is found to be primarily due to chain retraction after considerable stretching rather than chain orientation.
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Affiliation(s)
- Yuyuan Lu
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Shi-Qing Wang
- Department
of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States
| | - Zhen-Gang Wang
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
- Division
of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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27
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Cao J, Qin J, Milner ST. Simulating Constraint Release by Watching a Ring Cross Itself. Macromolecules 2014. [DOI: 10.1021/ma500325z] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jing Cao
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jian Qin
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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28
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Panagiotou E, Kröger M, Millett KC. Writhe and mutual entanglement combine to give the entanglement length. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062604. [PMID: 24483478 DOI: 10.1103/physreve.88.062604] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Revised: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We propose a method to estimate N(e), the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it works for both linear and ring chains, works under all periodic boundary conditions, does not require knowing the contour length of the primitive paths, and does not rely on a smooth set of data. We apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies.
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Affiliation(s)
- E Panagiotou
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - M Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - K C Millett
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
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30
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31
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Pestryaev EM. Molecular-dynamics study of chain reptation in a gel. POLYMER SCIENCE SERIES A 2013. [DOI: 10.1134/s0965545x13050052] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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32
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Affiliation(s)
- Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
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33
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Qin J, So J, Milner ST. Tube Diameter of Stretched and Compressed Permanently Entangled Polymers. Macromolecules 2012. [DOI: 10.1021/ma301830w] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Jungseob So
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
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34
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Abstract
The extreme sensitivity of rheology to the microstructure of polymer melts has prompted the development of “analytical rheology,” which seeks inferring the structure and composition of an unknown sample based on rheological measurements. Typically, this involves the inversion of a model, which may be mathematical, computational, or completely empirical. Despite the imperfect state of existing models, analytical rheology remains a practically useful enterprise. I review its successes and failures in inferring the molecular weight distribution of linear polymers and the branching content in branched polymers.
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Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
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35
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Everaers R. Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, and slip-link models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:022801. [PMID: 23005812 DOI: 10.1103/physreve.86.022801] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Revised: 06/18/2012] [Indexed: 06/01/2023]
Abstract
We show that the front factor appearing in the shear modulus of a phantom network, G(ph) = (1-2/f)(ρk(B)T)/N(s), also controls the ratio of the strand length, N(s), and the number of monomers per Kuhn length of the primitive paths, N(ph)(PPKuhn), characterizing the average network conformation. In particular, N(ph)(PPKuhn) = N(s)/(1-2/f) and G(ph) = (ρk(B)T)/N(ph)(PPKuhn). Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, N(e)(rheo) = (ρk(B)T)/G(e), should equal N(e)(PPKuhn). Assuming binary entanglements with f = 4 functional junctions, we expect that N(e)(rheo) should be twice as large as the topological entanglement length, N(e)(topo). These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.
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36
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van Ruymbeke E, Masubuchi Y, Watanabe H. Effective Value of the Dynamic Dilution Exponent in Bidisperse Linear Polymers: From 1 to 4/3. Macromolecules 2012. [DOI: 10.1021/ma202167q] [Citation(s) in RCA: 70] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- E. van Ruymbeke
- Bio and Soft
Matter, Institute on Condensed Matter and Nano-science, Université Catholique de Louvain, Louvain-la-Neuve,
Belgium
- Institute of Electronic Structure & Laser, FORTH, Heraklion, Crete, Greece
| | - Y. Masubuchi
- Institute for
Chemical Research, Kyoto University, Gokasyo,
Uji, Kyoto 611-0011, Japan
| | - H. Watanabe
- Institute for
Chemical Research, Kyoto University, Gokasyo,
Uji, Kyoto 611-0011, Japan
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37
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Affiliation(s)
- Windsor Bisbee
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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38
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Subramanian G. A topology preserving method for generating equilibrated polymer melts in computer simulations. J Chem Phys 2010; 133:164902. [DOI: 10.1063/1.3493329] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Rubinstein M. Polymer physics-The ugly duckling story: Will polymer physics ever become a part of “proper” physics? ACTA ACUST UNITED AC 2010. [DOI: 10.1002/polb.22135] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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40
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Hou JX, Svaneborg C, Everaers R, Grest GS. Stress relaxation in entangled polymer melts. PHYSICAL REVIEW LETTERS 2010; 105:068301. [PMID: 20868018 DOI: 10.1103/physrevlett.105.068301] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2010] [Revised: 05/25/2010] [Indexed: 05/29/2023]
Abstract
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.
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41
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Karayiannis NC, Kröger M. Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: methodology and performance. Int J Mol Sci 2009; 10:5054-5089. [PMID: 20087477 PMCID: PMC2808023 DOI: 10.3390/ijms10115054] [Citation(s) in RCA: 134] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2009] [Revised: 11/17/2009] [Accepted: 11/20/2009] [Indexed: 12/02/2022] Open
Abstract
We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.
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Affiliation(s)
- Nikos Ch. Karayiannis
- Institute for Optoelectronics and Microsystems (ISOM) and ETSII, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, E-28006 Madrid, Spain
| | - Martin Kröger
- Polymer Physics, Swiss Federal Institute of Technology, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8049 Zurich, Switzerland
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42
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Kivotides D, Wilkin SL, Theofanous TG. Entangled chain dynamics of polymer knots in extensional flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041808. [PMID: 19905334 DOI: 10.1103/physreve.80.041808] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2009] [Indexed: 05/28/2023]
Abstract
We formulate a coarse-grained molecular-dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in a strong extensional flow (Deborah number De=1.6 ). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the "natural," unraveling, and flow-induced chain motions. Moreover, the steady-state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.
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Affiliation(s)
- Demosthenes Kivotides
- Department of Chemical Engineering, Center for Risk Studies and Safety, University of California, Santa Barbara, California 93117, USA
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43
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Hoy RS, Foteinopoulou K, Kröger M. Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031803. [PMID: 19905139 DOI: 10.1103/physreve.80.031803] [Citation(s) in RCA: 201] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2009] [Revised: 06/22/2009] [Indexed: 05/28/2023]
Abstract
Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.
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Affiliation(s)
- Robert S Hoy
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA.
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44
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Foteinopoulou K, Karayiannis NC, Laso M, Kröger M. Structure, Dimensions, and Entanglement Statistics of Long Linear Polyethylene Chains. J Phys Chem B 2008; 113:442-55. [DOI: 10.1021/jp808287s] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Katerina Foteinopoulou
- Institute for Optoelectronics and Microsystems (ISOM) and ETSII, UPM, José Gutiérrez Abascal 2, E-28006 Madrid, Spain
| | - Nikos Ch. Karayiannis
- Institute for Optoelectronics and Microsystems (ISOM) and ETSII, UPM, José Gutiérrez Abascal 2, E-28006 Madrid, Spain
| | - Manuel Laso
- Institute for Optoelectronics and Microsystems (ISOM) and ETSII, UPM, José Gutiérrez Abascal 2, E-28006 Madrid, Spain
| | - Martin Kröger
- Polymer Physics, Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 10, CH-8093 Zürich, Switzerland
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45
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Wang Z, Larson RG. Constraint Release in Entangled Binary Blends of Linear Polymers: A Molecular Dynamics Study. Macromolecules 2008. [DOI: 10.1021/ma800680b] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zuowei Wang
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
| | - Ronald G. Larson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
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46
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Svaneborg C, Everaers R, Grest GS, Curro JG. Connectivity and Entanglement Stress Contributions in Strained Polymer Networks. Macromolecules 2008. [DOI: 10.1021/ma800018f] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Carsten Svaneborg
- Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Langelandsgade 140, DK-8000 Århus, Denmark, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672, Université de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France, Sandia National Laboratories, Albuquerque, New Mexico 87185, and Department of Chemical & Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131
| | - Ralf Everaers
- Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Langelandsgade 140, DK-8000 Århus, Denmark, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672, Université de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France, Sandia National Laboratories, Albuquerque, New Mexico 87185, and Department of Chemical & Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131
| | - Gary S. Grest
- Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Langelandsgade 140, DK-8000 Århus, Denmark, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672, Université de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France, Sandia National Laboratories, Albuquerque, New Mexico 87185, and Department of Chemical & Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131
| | - John G. Curro
- Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Langelandsgade 140, DK-8000 Århus, Denmark, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672, Université de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France, Sandia National Laboratories, Albuquerque, New Mexico 87185, and Department of Chemical & Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131
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47
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Hoy RS, Robbins MO. Strain hardening of polymer glasses: entanglements, energetics, and plasticity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031801. [PMID: 18517408 DOI: 10.1103/physreve.77.031801] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2007] [Indexed: 05/26/2023]
Abstract
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.
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Affiliation(s)
- Robert S Hoy
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA.
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48
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Uchida N, Grest GS, Everaers R. Viscoelasticity and primitive path analysis of entangled polymer liquids: From F-actin to polyethylene. J Chem Phys 2008; 128:044902. [DOI: 10.1063/1.2825597] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Sixou B. Molecular dynamics simulation of the first stages of the cavitation process in amorphous polymers. MOLECULAR SIMULATION 2007. [DOI: 10.1080/08927020701502057] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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50
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Shanbhag S, Park SJ, Zhou Q, Larson RG. Implications of microscopic simulations of polymer melts for mean-field tube theories. Mol Phys 2007. [DOI: 10.1080/00268970601143333] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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